SOLUTION: The equation sin x = csc x ______
has two solutions with the interval 0° ≤ x ≤ 360°
has no solution
has two solutions within the interval 0° ≤ x ≤ 180°
is a
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-> SOLUTION: The equation sin x = csc x ______
has two solutions with the interval 0° ≤ x ≤ 360°
has no solution
has two solutions within the interval 0° ≤ x ≤ 180°
is a
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Question 1182117: The equation sin x = csc x ______
has two solutions with the interval 0° ≤ x ≤ 360°
has no solution
has two solutions within the interval 0° ≤ x ≤ 180°
is an identity Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!
sin(x) = csc(x)
sin(x) = 1/sin(x)
sin^2(x) = 1
sin^2(x)-1 = 0
(sin(x)-1)(sin(x)+1) = 0
sin(x)-1 = 0 or sin(x)+1 = 0
sin(x) = 1 or sin(x) = -1
If we solved the first equation for x, we would get x = 90. Use the unit circle.
This means sin(90) = 1.
Also, you should find that sin(270) = -1 through the unit circle.
The two solutions on the interval 0° ≤ x ≤ 360° are x = 90 and x = 270
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